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The general solution of the DE (dy)/(d...

The general solution of the DE ` (dy)/(dx) = ( y^(2)- x ^(2))/( 2xy )` is

A

` x ^(2) - y ^(2) = C _1 x `

B

`x ^(2) + y ^(2) = C_1 y `

C

`x ^(2) + y ^(2) = C_1 x `

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
The given De is homogeneous. Put `y = v x and (dy)/(dx) = v + x (dv)/(dx) `.
` therefore int ( 2v)/( ( 1+ v ^(2))) dv = - int (1)/(x) dx rArr log ( 1 + v ^(2) ) + log x = log C `
` therefore x ^(2) + y^(2) = C_1 x`.
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